A technique called "fuzzy logic," developed by Dr. Lotfi Zadeh and described in "Fuzzy Sets," Information and Control, Vol. 8, No. 3, June 1965, pp. 338-53, has proven highly effective in controlling complex systems. Using fuzzy logic, input variables are processed against a collection of rules, each of which expresses a system objective in propositional form; for example: "if velocity is low and rpm is low then shift to 1st gear." Unlike conventional logic, in which conditions are either satisfied or not satisfied, the conditions "velocity is low" and "rpm is low" may be only partially satisfied so that the rule is only partially satisfied.
The use of fuzzy logic, however, may require a substantial amount of memory. The use of numerous rules in a rule set, often the result of the use of the "matrix" approach, or the employment of detailed nonlinear membership functions, may cause a strain on memory resources. There are many applications in which such resources are not plentiful, or in which key parameters should be stored so that they are readily accessible (e.g., in non-volatile memory rather than read-only memory while the control function is still being developed and calibrated). In these cases, it may be advantageous to have a more parsimonious implementation which supports the functionality of fuzzy logic, yet bend some of its principles.
In particular, in order for the typical (Mamdani "Max-Min" algorithm) fuzzy logic control algorithm to produce a useful variation of the output, it is necessary to have more than one rule. Variation of output is obtained by the consequents of two (or more) rules playing against each other. A side effect of this method of generating variation in output is the difficulty in producing an explicit output value for particular values of inputs. If the desired output is known for specific inputs, some experimentation and iteration is needed to obtain the necessary membership functions that yield the desired relationship.
For these reasons, there exists a need for a variation of the usual fuzzy logic algorithm in which the parameterization is more compact and the relationship between the output function and the input signals is more explicit.